Allow brisket to come to room temperature about an hour before you are ready to smoke.
Pat brisket dry with paper towels.
Drizzle with olive oil, coating all sides.
In a bowl combine brown sugar with granulated garlic, onion powder, granulated garlic, green chile powder, thyme, smoked paprika, salt, pepper and dry mustard.
Sprinkle rub all over brisket.
With a sharp knife, pierce the brisket all over, pushing the olive oil and rub down into the meat, all over.
Prepare a grill fire or smoker to about 325° with hickory or oak chunks.
Cook brisket fat side down with the grill closed. Keep the temperature between 300° to 325°.
Continue to cook the brisket until it reaches just over 200° about 5 - 6 hours.
If you feel like the brisket is getting dry, you can remove it after it hits about 165°-170°, you can wrap it in peach butcher paper or heavy foil and continue to cook.
Remove from grill and rest one hour before slicing.